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Material and Structures
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Materials and Structures ISSN 1359-5997Volume 48Number 10 Mater Struct (2015) 48:3367-3375DOI 10.1617/s11527-014-0405-5
Falling-weight impact response forprototype RC type rock-shed with sandcushion
Abdul Qadir Bhatti
1 23
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ORIGINAL ARTICLE
Falling-weight impact response for prototype RC type rock-shed with sand cushion
Abdul Qadir Bhatti
Received: 27 September 2012 / Accepted: 19 August 2014 / Published online: 11 October 2014
� RILEM 2014
Abstract In this paper, a prototype model of rein-
forced concrete (RC) type rock-shed is numerically
examined by means of three-dimensional elasto-plastic
finite element based model of RC rock-shed structure,
having sand cushion, against the impact of 10 ton heavy
weight. This study is undertaken in order to improve the
knowledge for establishing a rational performance-
based impact resistant design procedure for the RC type
rock-sheds. Following results are obtained from this
study: (1) the model fails in the punching shear mode
when surcharged at the center of roof slab; and (2) the
impact resistant capacity of the free edges of the model
is greater than that at the center, as the free edges can
behavemore flexibly and absorb more impact energy in
comparison with the center of the roof slab.
Keywords Rock-shed � Dynamic nonlinear
analysis � Sand model � Ultimate state � Input impact
energy
1 Introduction
Protection galleries are normally constructed along
the highways in mountainous areas. Rock fall
protection galleries are an efficient measure to
protect roads and railways, mainly if the danger is
locally concentrated. Rock fall in the mountainous
areas is one of the natural hazards which occur due
to strong typhoon, snow avalanches and landslides.
The associated risks due to rock falls are usually
managed by means of structures such as galleries
protecting roads and railways.
A study on the rock fall galleries has shown that
most of the existing galleries consist of reinforced
concrete slabs and are covered with a cushion layer [1,
2]. The cushion layer distributes the contact stresses,
reduces the accelerations in the striking body and
increases the impact time. Normally, granular sand
from the surroundings or gravel is used as cushion
layer. Protection galleries typically span 9 m with a
slab thickness of approximately 0.70 m. The back side
of the galleries is clamped and is supported at the
retaining wall as shown in Fig. 1.
A. Q. Bhatti (&)
Department of Earthquake Engineering, School of Civil
and Environmental Engineering, National University of
Sciences and Technology (NUST), Islamabad, Pakistan
e-mail: [email protected]; [email protected];
A. Q. Bhatti
Pacific Earthquake Engineering Research Centre (PEER),
University of California, Berkeley, USA
A. Q. Bhatti
Department of Structural and Geotechnical Engineering,
Politecnico di Torino, Corso Duca degliAbruzzi 24,
10129 Turin, Italy
A. Q. Bhatti
Department of Civil Engineering, Islamic University,
Madina, KSA
Materials and Structures (2015) 48:3367–3375
DOI 10.1617/s11527-014-0405-5
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However, usually those shelters have been designed
without considering impact loads due to falling rocks.
In order to establish a rational impact resistant design
procedure for RC type rock-shelter [3], based not only
on allowable stress design but also on ultimate state
design and/or performance based design method, the
impact resistant capacity and/or maximum input impact
energy for the RC structures must be clearly estimated.
At present, the RC structures have been designed
statically based on allowable stress design method.
In recent years, numerical modeling of various
concrete structures under impact loads has been inves-
tigated by using finite element model/discrete element
model (FEM/DEM and few combined. Hence, many
FEM/DEM models for the pre-failure and post failure
transient dynamics of reinforced concrete structures
under impact loading have been developed [2, 4–6]. For
such models, maximum input impact energy for reach-
ing ultimate state was numerically estimated by means
of three-dimensional elasto-plastic finite element
method for existing real RC rock-shelters with sand
cushion under falling heavy-weight impact loading [6–
8] To effectively absorb and disperse the impact forces,
caused due to a rock falling, a cushionmaterial has been
developedwhich is composed of 90 cm thick sand layer
(top) and 20 cm thick gravel as confined material [9].
For numerical analysis, LS-DYNA code was used [10].
The dimension of the RC shelter is 9,000 mm in length,
4,700 mm in height of side-wall and 4,000 mm in
width. 10,000 kg steelweightwas used as fallingweight
having falling height of 20, 50, 100, 150, 200, 250 m. In
this numerical analysis, solid elements were employed
for concrete, falling heavy-weight and sand-cushion,
and beam elements for reinforcing steel. Drucker–
Prager and reinforcing steel yield criteria were used as
material constitutive law for concrete and reinforcing
steel, respectively. Cracks were estimated by allowing
tensile stress cut-off at reaching at the tensile strength. In
this paper, weight impact force, total axial force at the
side walls, displacement wave at the loading point and
crack patterns of the shelter at the time of occurrence of
maximum displacement are outputs [11–13].
The results obtained from this study are as follows;
(1) The serviceability and ultimate limit states were
determined from various cases having energies of
0.196, 2.45, 4.90, 7.35, 9.8 and 12.3 MJ. (2) It was
observed that maximum response generation time of
the impact force and displacement is different for
various input energies. (3) Maximum input impact
energy for reaching ultimate state was numerically
examined by means of three-dimensional elasto-
plastic FE method for RC rock-shed.
2 Outline of prototype RC type rock-shed
The cross-section and absorbing system of the RC rock-
shed are shown in Fig. 1. The geometry of the rock-shed
and height of sidewall beamare shown inFig. 2.TheRC
type rock-shed used for analysis is about 1/2 scale of
prototype and is assumed to be 11,100 mm in length and
7,000 mm height respectively.
In themodel, D32 reinforcing steel for each upper and
lower axial ones were arranged having 100 mmconcrete
cover. The shear re-bars were not used in this study as
shown in Fig. 3. A rectangular shape footing was
constructed so as to be close to perfectly fixed supports,
Fig. 1 RC rock-shed
Fig. 2 Geometry of rock-shed
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as much as possible. The displacement of the slab was
measured at the mid span and impact force P was
estimated using contact force between heavy-weight and
rock-shed [14]. The material properties of concrete, re-
bars, sandandgravel duringanalysis are listed inTable 1.
3 Numerical overview
3.1 FE models
An example of FE numerical analysis model is shown
in Fig. 4. Only half of RC arch tunnel model and
footing, a falling heavy-weight, and a half of support-
ing apparatus were modelled with FE meshes consid-
ering two symmetrical axes. Six and eight node solid
elements were used in the FE model except for axial
and shear reinforcing steel in the footing. Finite
element models with reinforcing steel arrangement are
shown in Fig. 4 [15, 16]. Total number of nodes and
Fig. 3 Details of steel reinforcement
Table 1 Material properties of rock-shed system
Material type Density Elastic
coefficient
Poisson’s
ratio
q (kg/m3) E (GPa) m
RC 2,500 25 0.2
Sand 1,760 10 0.06
Concrete 2,350 13.7 0.167
Reinforcing steel 7,690 206 0.3
Gravel 1,860 0.042 0.45
Falling weight 3,054 210 0.3
Fig. 4 Finite element mesh and reinforcing steel details of
numerical model
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elements of the RC rock-shed model are shown in
Fig. 4 are 128,890 and 88,882 respectively. Numerical
analyses models were precisely formed for each
component based on the dimensions of the RC rock-
shed tunnel model used in the real prototype structure.
However, axial reinforcing steels have been sim-
plified as a square element rather than simple circular
reinforcing steel, having equivalent cross sectional
area of specific round reinforcing steels. Contact
surface is defined between supporting device and
concrete surface; and between striking face of heavy-
weight and concrete surface, in which sliding with
contact and separation can be considered in this
contact surface applied here [17–19]. All nodes among
concrete and axial reinforcing steel were assumed to
be perfectly bonded with each other. Impact force is
numerically surcharged against the RC rock-shed by
adding a predetermined impact velocity to all nodes of
falling heavy-weight which is set on the surface of RC
rock-shed model. Impact response analysis for RC
rock-shedmodel was performed up to 300 ms from the
beginning of impact. The time increment for numer-
ical analysis is almost equal to 0.6 ms which is
determined based on Courant stability condition. The
typical numerical cases are listed in Table 2.
3.2 Modelling of materials
Figure 5 shows the stress–strain relations for each
material: concrete and reinforcing steel. Neither strain
rate effects of concrete and reinforcing steel elements
nor softening phenomenon of the post peak of concrete
were considered for this elasto-plastic impact response
analysis technique. However, to accurately simulate a
damped free vibration of the RC arch tunnel model
after the rebound of heavy-weight, a damping constant
h was considered. The constitutive law for each
material characteristic is briefly outlined below:
3.2.1 Concrete
Stress–strain relation of concrete was assumed by
using a bilinear model in the compression side and a
cut-off model in the tension side as shown in Fig. 5b. It
is assumed that: (1) yielding stress is equal to the
compressive stress f’c which is equal to-20 MPa; (2)
concrete yields at a strain of 0.0015; (3) the tensile
stress is perfectly released when an applied pressure
reaches the tensile strength of concrete; and (4) the
tensile strength is set to be 1/10 of the compressive
strength. Von Mises criterion was applied to the
yielding of concrete [2]. LS-DYNA material model
MAT_SOIL_AND_FOAM_FAILURE was used to
model the concrete elements [6].
3.2.2 Reinforcing steel
For main reinforcing steels an elasto-plastic model
following isotropic hardening rule was applied as
shown in Fig. 5c. Here, the plastic hardening modulus
H’ was assumed as 1 % of young’s modulus (Es). The
yielding condition was judged based on von Mises
criterion. LS-DYNA material model MAT_PLAS-
TIC_KINEMATIC was used to model main and shear
reinforcing steel.
3.2.3 Falling heavy-weight, and anchor plate
The other elements (heavy-weight and anchor plate)
were modelled as elastic body based on experimental
observations. Young’s modulus and Poisson’s ratio
were assumed as 206 GPa and 0.3, respectively. LS-
DYNA material model MAT_ELASTIC was used to
model them.
3.2.4 Sand cushion
Figure 3a shows the constitutive model for sand
cushion. To rationally analyze the stress behaviour
of sand cushion when a heavy-weight collides, second
order parabolic stress–strain relation for sand cushion
[2] was applied in which the constitutive relation is
described in the following expression.
rs ¼ 50e2s ð1Þ
Table 2 Properties and case types of rock-shed system
Case type Falling height
(m)
Impact
(kN)
Location Energy
(MJ)
E-0.2 20 9.8 Centre 0.196
E-2.5 50 49.0 2.45
E-4.9 100 4.90
E-7.4 150 7.35
E-9.8 200 9.80
E-12.3 250 12.3
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Here, rs is stress in sand and es is the volumetric strain
of sand element. The material properties of sand for
impact response analysis were assumed as; Young’s
modulus Es = 10 GPa; Poisson’s ratio; ms = 0.06 and
density qs = 1,600 kg/m3. LS-DYNA material model
MAT_CRUSHABLE_FOAM was used [2].
3.2.5 Strain rate effects and viscous damping constant
Neither strain rate effects of concrete and reinforcing
steel nor softening phenomenon at post-peak of
concrete were considered for impact response analysis
of the RC rock shed models. The post peak softening
of concrete was not considered. Due to low velocity
impact there is no effect on the results [5–7]. In
addition, to accurately simulate impact response
characteristics of the RC rock shed models, a viscous
damping constant h was considered.
4 Overview of numerical results
4.1 Timehistories of impact force anddisplacement
at crown
The numerical analysis results for time histories of
impact force (P) are shown in Fig. 6. The six types
such as E-0.2, E-2.5, E-4.9, E-7.4, E-9.8 and E-12.3
having energies of 0.196, 2.45, 4.90, 7.35, 9.8 and
12.3 MJ respectively were analyzed as shown in
Table 2. The impact force (P) obtained from the
numerical analysis were estimated by summing the
contact reaction forces in the perpendicular direction
caused in the contact interface elements of falling
heavy-weight.
From these figures, it can be observed that the
impact force wave (P) for each case is composed of
few half-sinusoidal waves: an incidental wave having
extremely short duration at the beginning of impact
with high frequency contact within 10 ms; and one
and/or two waves having relatively larger duration
from 10 to 40 ms. The configuration of the wave in
numerical analysis is similar for all cases of increased
input energy. By comparing the impact forces with
impact energy it seems that the former increases with
increase in impact energy. However it is observed that
the time history has varying time duration cycle with
increase in input energy.
In addition, when paying attention to the maximum
impact force after falling weight collides, the genera-
tion time for the main impact wave is 20 ms in case of
E-9.8 and E12.3 but for other cases it is between 20 and
30 ms. The main wave motion shows that the tendency
of dissipation time becomes short with the increase of
input energy and amplitude. For example, in the case of
E-2.5, the continuation time is 25 ms (ms), as compared
to 15 ms in the case of E-12.3, showing a decreasing
trend. Moreover, in the case of E-2.5 the amplitude of
the wave is 5 MN, which is increased by about 5 times
to 25 MN grade in the case of E-12.3. The relation
Fig. 5 Stress strain
relationship of material
models for sand, concrete,
steel
Fig. 6 Impact force time history cases
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between input energy and the maximum impact force is
shown in Fig. 7 indicating a linear relation with respect
to input energy.
Focusing on the displacement shown in Fig. 8, it is
seen that the vibration period after reaching maximum
amplitude vary from 25 to 75 ms. The maximum
displacements for E12.3 case is about 28 mm. The RC
rock-shed vibrate with smaller residual displacement
in case of E-2.5. On the other hand, it is observed from
the numerical analysis results that the RC rock-shed
vibrate as continuous body with larger residual
displacement and high damping after suffering severe
damages. The main reason may be that diagonal shear
cracks occurred near footing and de-bonding of re-bars
from concrete cannot be precisely estimated due to the
assumptions of continuous body and perfect bond
between reinforcing steel and concrete. At the begin-
ning of 10 ms of displacement waveform there is no
significant amplitude and from 20 to 30 ms the
maximum response is observed in all cases of input
energy. Between 70 and 80 ms there is negative
displacement due to rebound of the falling weight
impact. The relationship between residual displace-
ment and input energy remains linear from E-2.5 to
E-12.3 as shown in Fig. 9. However, there is sudden
increase in slope from E-9.8 to 12.3 due to severe
damage occurs when input energy is quite large.
The strain measured at steels located in the top slab
of reinforcement are shown in Fig. 10 for various
cases. Since in the case of E-7.4, E-9.8 and E-12.3, the
strain is exceeding -1,500 microstrains, which is a
plastic level for concrete element as shown in Fig. 5b.
The case of E-7.4 can be used as serviceability limit
state and E-12.3 can be used as performance limit
state. Moreover, it shows that the strain value of
E-12.3 becomes about 2.5 times more that the value as
in case of E-9.8. It is observed that that tendency of
plastic hardening is higher with increase in input
energy.
Fig. 7 Relationship between impact force and input energy Fig. 8 Displacement Time History Cases
Fig. 9 Relationship between residual dispalcement and input
energy
Fig. 10 Strain time history in reinforcing steel cases
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4.2 Crack patterns of side surface of concrete
Based on a constitutive law model assumed for
concrete elements earlier, stress applied in the con-
crete elements will be converted to zero when the
applied pressure in an element reaches the tension cut-
off value. In other words, it is understood that the
element with zero stress has a potential for crack
occurrence. Here, crack patterns can be predicted
based on this concept and the applicability of the
prediction method was discussed by comparing the
crack patterns obtained from experimental results.
Figure 11 shows the contours of the maximum
principal stress at the maximum displacement obtained
Fig. 11 Crack pattern of rock-shed for case types
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from numerical analysis and crack pattern developed on
side-surfaces of the RC rock-shed. In those figures,
white colour stress contour means that the elements are
around zero stress. From those comparisons, it is seen
that the crack patterns observed from rock-shed can be
increased by the increase in input energy. The crack
distributions at the top of slab and around the thickness
are shown in Figs. 11a–e. Major cracks occurred in the
case of E-12.3. When the input energy is small, it is
observed that the compression stress has occurred in the
longitudinal direction. However with increase in input
energy, the compression stress decreases.
5 Conclusions
Applying cushion material is one of the engineering
approaches to ensure the greater safety of important
structures, such as nuclear power plants, fuel tanks,
and rock-shelters. In this study, focusing on the
absorbing system developed for rock-sheds con-
structed over the highways in mountains areas and
along the edge of cliff near seaside, establishment of
a numerical analysis method for this type of system is
developed. Numerical analysis method is proposed to
investigate a rock-shed by performing the falling-
weight impact load FE analysis of prototype RC
rock-shed. The results obtained from this study are as
follows:
1. Residual displacement and input energy
increase linearly but after the case of impact
energy of 9.MJ (E-9.8), it suddenly increases
due to major damage occurred at the top of the
rock-shed.
2. It seems clear that till the case of impact energy
of 7.5 MJ (E-7.5), the rock-shed reached its
ultimate limit state. It can be concluded from
the impact force time history, displacement time
history and crack pattern as shown in Figs. 6, 8,
and 11 respectively, that the case of impact
energy of 7.4 MJ (E-7.4) may be used as the
serviceability limit state and impact energy of
12.3 MJ (E-12.3) may be used as performance
limit state.
3. Here maximum input impact energy for reaching
ultimate state was numerically examined by
means of three-dimensional elasto-plastic FE
method for RC rock-shed designed based on
allowable stress design concept.
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